Every time in edit mode when I select a group of vertices and hit “selection to cursor,” instead of keeping the vertices as a distinct group like every single other transformation in the entirety of blender, for no reason it moves all vertices to the singular location of the cursor, effectively merging them, instead of simply moving the average of the location of the group like a normal transformation.
Try Selection to Cursor (Offset).
It does exactly like expected. It will move all selected vertices to the cursor in edit mode. When you do this in object mode, however, it will leave your object intact.
You are using the wrong command. Selection to cursor literally moves each individual vertex to the spot the cursor is on. What you want is Selection to Cursor (with offset). This preserves their position relative to each other when moved to the cursor.
I can’t think of what you’d use this for in 3d view, but in the UV/image editor you might want some of the islands to have a single color. You can do this by moving all the verts for those islands to a pixel with that color in the image.